WORKING P A P E R

Self-Dealing and Compensation for Financial Advisors

JOANNE YOONG ANGELA A. HUNG

WR-713

September 2009

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Self-Dealing And Compensation For Financial

Advisors∗

Joanne Yoong and Angela Hung

September 30, 2009

Abstract

Recent legislative and regulatory activity related to investmentadvice in 401(k) plans has focused on the issue of self-dealing. Inthis paper, we develop a framework that addresses questions of self-dealing based on the direct-marketing model introduced by Inderstand Ottaviani (2009). We specifically adapt the model to the settingof 401(k) plan advice, extend the theoretical framework to considerthe implications of financial literacy and discuss various key aspects ofexisting and proposed 401(k) advice legislation in the context of themodel’s predictions.

∗This research was supported by funds from the Department of Labor. We thank JeffDominitz, Prakash Kannan and Juergen Maurer for related work and insightful discussion.The findings and conclusions expressed are solely those of the authors and do not representthe views of DOL, NIA, any agency of the Federal Government, or the RAND Corporation.The authors are responsible for all errors and omissions.

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1 Introduction

Recent legislative and regulatory activity related to investment advice in

401(k) plans has focused on the issue of self-dealing. A common example of

self-dealing arises if an advisor who works for a particular provider deliber-

ately advises plan participants to purchase the provider’s mutual funds in

order to realize a sales commission or other benefits, without regards to their

suitability. In this paper, we develop a framework that addresses questions of

self-dealing based on the direct-marketing model introduced by Inderst and

Ottaviani (2009) to analyze optimal incentive structures within the context

of participant-directed defined contribution(DC) plans, with respect to issues

such as financial advisors who are also plan managers, regulations related to

advisor qualifications and compensation, incentive effects of future advising

services beyond the plan itself, and the combination of other features such

as automatic enrollment with advisory services. In this framework, a firm

employs agents with two distinct tasks: approaching new customers as well

as advising on the product’s suitability. In this setting, the incentives needed

to induce agents to search for new customers may also subsequently tempt

them to advise inappropriate products.

In what follows we specifically adapt the model to the setting of 401(k)

plan advice. We then extend the theoretical framework to consider the impli-

cations of financial literacy, which is not explored in the existing literature,

and apply the model to the analysis of various aspects of proposed 401(k)

advice legislation.

2 Background

2.1 Investment Advice and Self Dealing in 401(k) Plans

Under Section 3(21)(A)(ii) of ERISA, a “fiduciary” includes, inter alia, any

person that renders investment advice for a fee or other compensation, di-

rectly or indirectly, with respect to any moneys or other property of an

ERISA plan, or has the authority or responsibility to do so. The prohib-

ited transaction rules of ERISA prevent self-dealing by barring fiduciaries

2

from giving advice to participants regarding any investments that would

result in the payment of additional fees to themselves (or their affiliates).

This rule effectively limited mutual fund companies who were plan providers

from offering advice to participants. However, as recent research has amply

demonstrated, many 401(k) plan participants are not sufficiently prepared

to manage their own investment accounts without support. As a first step,

in 1997, the Department of Labor (DOL)’s Interpretive Bulletin (I.B. 96-1)

identified specific categories of investment-related materials that did not con-

stitute advice, but could be regarded as “education”. To qualify, these would

have to be restricted to generalized financial information and non-specific as-

set allocation models.

Under I.B. 96-1, plan providers were still be barred from offering partic-

ipants individualized, one-on-one advice. In 2001, DOL Advisory Opinion

(AO) 2001-09A (a letter to SunAmerica Inc) noted that the provision of

fiduciary investment advice would not constitute a prohibited transaction

if it resulted from the application of methodologies developed, maintained

and overseen by an independent party. This AO resulted in the growth of

a number of third-party structures which became known as SunAmerica ar-

rangements, under which a provider would contract with another financial

institution (such as Financial Engines, Inc and Ibbotson Associates, Inc) to

provide advisory services.

Industry participants continued to propose several reasons for increas-

ing plan providers’ ability to directly give advice. Some argued for tech-

nical efficiency and complementarities, suggesting that detailed information

about participants and pre-existing administrative platforms would enable

providers to give better quality recommendations at lower cost than inde-

pendent advisors. Others noted that reputational incentives could naturally

constrain self-dealing, as opportunities to manage future rollover assets would

provide a strong incentive for advisors to maintain good relationships with

investors (J.P. Morgan(2004)).

A more significant step was taken in 2006, when the Pension Protection

Act (PPA) amended ERISA by adding a new statutory prohibited transac-

tion exemption that would also allow “eligible investment advice arrange-

ments”. An “eligible investment advice arrangement” would be an arrange-

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ment that (i) used a level-fee compensation structure that did not vary de-

pending on the basis of any investment option selected; or (ii) used a unbiased

computer model that met a number of statutory requirements. In addition,

DOL clarified that a fiduciary’s affiliate generally would be subject to the fee-

leveling limits only if that affiliate itself provided advice to plan participants.

The PPA would therefore effectively allow the provider to directly offer advice

without an intermediary, subject to several reviews and restrictions including

approval by a separate plan fiduciary, annual audits and various disclosure

requirements.

Responses from interested parties solicited by DOL argued that the fi-

nancial industry would still be highly constrained by the language of the

statutory exemption. For instance , under the PPA, in addition to being un-

biased, the computer model must use generally accepted investment theories,

utilize relevant participant information (which may include age, retirement

age, life expectancy, risk tolerance), and take into account the full range

of investments, including equities and bonds, in determining the investment

portfolios of the beneficiary. Financial industry representatives argued that,

given the wide range of allowable investments, models that conformed to

these requirements in their strictest sense would be highly infeasible.

In August 2008, DOL proposed regulation implementing the PPA that

included an additional class exemption with two important features. Firstly,

the proposed class exemption would permit advisors to provide individualized

advice to a worker after giving advice generated by use of a computer model

and would permit advice that might generate greater income for the advisor

and his/her affiliates if the advice were found to be in the best interest of

the worker. Secondly, the level-fee arrangement would apply only to the

individual advisor and not to his or her firm. In January 2009, DOL issued

this regulation as a Final Rule, to be effective March 2009.

However, new developments have moved sharply in the opposing direc-

tion. In particular, recent stock market volatility, skepticism about the cred-

ibility of financial institutions and large observed drops in the value of retire-

ment savings portfolios overall have raised concerns about unsuitable high-

margin overly-risky investments being sold to unsophisticated participants.

At the request of the entering Obama administration, DOL drew out the

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applicability and effective dates of the final regulation from March 23 to

May 22. On May 21st, the DOL announced a second extension for public

comments on the final regulations, until November 18, 2009.

In April of 2009, the House Education and Labor Committee Chairman

George Miller introduced the 401(k) Fair Disclosure for Retirement Security

Act of 2009 to Congress. The Act would repeal the investment advice pro-

vision enacted in the PPA and also prohibit several practices existing prior

to the PPA. Specifically, the investment advisor must not be the plan invest-

ment provider, must satisfy the pre-PPA level fee rule, and must comply with

other requirements including disclosure of indirect benefits. Alternatively, it

allows the provision of advice by a computer model under the existing PPA

rules, with additional restrictions. SunAmerica arrangements would be dis-

allowed unless the independent third party accepted fiduciary responsibility

or if the computer model were to adopt the PPA rules, including rules gov-

erning the asset universe to be including and annual audits. The Act also

eliminates managed accounts, whereby advice is automatically implemented

pursuant to a participants prior authorization. On June 24, 2009, the House

Education and Labor Committee reported out a bill (H.R. 2989) basically

incorporating Congressman Miller’s proposals, with some modifications. At

the time of this draft, H.R. 2989 remains pending.

2.2 Previous Theoretical Work

The theoretical literature related to financial advice is quite rich, but offers

surprisingly little that is directly relevant to the issues described above in the

context of self-dealing. A large body of work focuses attention on risk-sharing

between advisors and advisees (see, for example Golec (1992),Coles, Daniel,

and Naveen (2006),Das and Sundaram (2002),Golec and Starks (2004)),

rather than the issue of conflict of interest on the part of the advisor.

Building off the seminal work of Crawford and Sobel (1982), more re-

cent research has addressed the advisor-advisee relationship in the context of

strategic information transmission. This line of research examines the design

of optimal compensation contracts and the costs/benefits of delegation when

advisors have private information about advisees (see for example Liu (2005),

5

Krishna and Morgan (2008) ). In most of these papers, however, advisor bias

is specified exogenously. These models are not informative for an analysis of

how incentives or organizational structures themselves induce or reduce bias.

To model self-dealing in 401(k) plans, we instead adapt a model of direct

selling from the work of Inderst and Ottaviani (2009), in which we consider

agents who have to be simultaneously motivated to sell but also to not missell

products. In their approach, they highlight the agency problem between

a firm and its own agents, and the role of potential policy interventions

when the targeted action is carried out by agents rather than the firm itself.

This model has important implications for various settings where consumers,

product providers and advising agents interact.

Finally, most of the theory literature ignores investor heterogeneity due to

financial literacy (A key exception is Ottaviani (2000)). Yet, financial literacy

is a key element of the policy debate : individuals who are more literate

may benefit from additional information, but the concern is for individuals

who are more susceptible and hence more likely to be taken advantage of. In

what follows, we make a simple extension to the existing framework to include

naive and sophisticated investors, and to demonstrate that this heterogeneity

can have meaningful implications for outcomes as well as potential policy

interventions.

3 Model

Consider a risk-neutral firm which is a pension plan provider. The firm

sells one product, an equity mutual fund at price p, through a risk-neutral

agent, who promotes the company’s mutual fund to plan participants while

also recommending the appropriate asset allocation between the mutual fund

and a risk free asset, cash.

3.1 Participants

Plan participants have two investment-relevant types, θ = l, h, and derive

utility from the investment product based on type, where θh > 0 > θl. θ may

be thought of as based on risk preferences and other considerations, where

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only the high type h benefit from buying the provider’s funds and the low

type l benefit from simply holding cash.The participant does not know his

own type with certainty, but has the prior q = Pr[θ = h].

Based on the prior alone, the participant’s expected utility from the prod-

uct is quh + (1 − q)ul. We assume that quh + (1 − q)ul < 0, implying that

with this initial belief, participants will not buy the fund even at a zero price;

there will be no investment.

3.2 Multitask Agents

We use the terminology of Inderst and Ottaviani (2009) to describe the

agent’s two tasks : the agent firstly has to approach new customers (“prospect-

ing”) and then give them recommendations about whether to buy the fund

(“advising”).

For the “prospecting” task, the agent can choose to expend effort at a

private cost cs > 0 in order to contact a potential participantand encourage

them to contribute, after which participants decide with probability μ to

invest their funds in the plan.

However, participants who decide to invest are imperfectly informed about

the most appropriate investment mix, and hence rely on the agent to make

recommendations based on his private assessment. For the “‘advising” task,

the agent can therefore further expend effort to privately observe a signal

about the customer’s type s ∈ [0, 1] at a private cost ca > 0 and a firm

resource cost of k > 0. The agent then reports a recommendation r(s) where

r(s) = 1 if the agent’s recommendation is to buy the fund and r(s) = 0 if

not.

The signal is realized according to the type-dependent distribution Fθ,

where Fh dominates Fl in the monotone likelihood ratio order. The uncon-

ditional distribution of the signal, F (s), may be characterised as a function

of the prior probability and the type-dependent densities, where we define

f(s) = qfh(s) + (1 − q)fl(s). We assume that each density function fθ(s)

is continuous and strictly positive for s ∈ (0, 1), which allows us to assume

a strictly increasing posterior probability q(s) = Pr[θ = h|s]. We further

assume the boundary conditions fh(1) > 0, fl(0) > 0, and fh(0) = fl(1) = 0,

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such that extreme signals are fully informative: q(0) = 0 and q(1) = 1.

3.3 Financial Literacy

In this setting, to capture the concern that financially illiterate individuals

are susceptible to misguided advice, we model participant response to ad-

vice. The sophisticated consumer internalizes the advice process, and for

any anticipated signal s, weights the recommendation of the advisor accord-

ingly into his expected utility u(s), such that u(s) = q(s)uh + (1 − q(s))ul,

regardless of r(s). The sophisticated consumer therefore believes with some

probability that the advisor’s recommendation may not be suitable. How-

ever, financially-illiterate individuals may be naive or display other types

of behavioral biases. A naive consumer takes any recommendation at face

value, as an indication that they are in fact a high type i.e. u(s) = uh if

r(s) = 1 and u(s) = ul if r(s) = 0.

We first derive the results for consumers that are financially literate and

then explore the implications of financial illiteracy. The results presented

throughout reflect financially-literate consumers unless otherwise specified.

Note that the terms “sophisticated” and “financially-literate” interchange-

ably.

3.4 Penalties For Misselling

In their model, Inderst and Ottaviani (2009) also allow for an ex-post signal

about the quality of the match. In this case, consider that plan participants

who are unsatisfied with the performance of their mutual funds may lodge

a complaint with the fiduciary, the plan provider; or alternatively, a regular

audit of advisor activity may result in the discovery of misselling to unsuitable

types 1.

We define 0 < φ < 1 to be the probability of a verifiable audit or com-

plaint after the sale of a fund to a low type, θl. We assume that if a com-

plaint is received, the provider is liable for an exogenously determined fine or

1In an analysis focused on self-dealing, we do not examine the case in which high typesare not sold the funds, although they would have benefited from holding them

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penalty. This may capture direct costs and penalties e.g. fines or legal fees,

or indirect costs such as reputation (as emphasized by providers in real life).

We denote the expected value of penalties from selling to a θl participant to

be ρ.

3.5 Advisor Compensation Scheme

When deciding how to compensate the advisor, the provider observes neither

their activities nor the participants’ type. The provider observes only three

outcomes and can therefore in theory pay three separate levels of compensa-

tion.

1. No sale = w1

2. Sale, without complaint = w2

3. Sale, with a complaint = w3

We assume that the advisor is protected by limited liability and can never

receive less than zero compensation in any case, so w1, w2, w3 ≥ 0. We further

normalize the value of the outside option for the advisor to be 0.

3.6 Timing

The full interaction between the plan provider, the advisors and the partici-

pant proceeds as follows

• The plan provider sets the price p for their mutual fund product

• The provider sets the compensation scheme (w1, w2, w3) for the advisor

• The advisor chooses whether to exert initial effort to approach the

participant

• If yes, the advisor expends cs and participant becomes interested with

probability μ

• The advisor chooses whether to exert effort to advise the participant

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• If yes, the advisor evaluates the participant with private cost ca and

firm cost k, observing the signal s about their type

• The advisor makes a purchase recommendation

• The participant decides whether or not to purchase mutual funds at

price p

• If a θl participant purchases the fund product inappropriately, a viola-

tion is observed with probability φ and the provider pays an expected

penalty of ρ.

• The advisor receives compensation based on the realized outcomes.

4 Compensation-Setting

This setup is particularly suited to the analysis of regulating compensation

and misselling, as the advisor’s preferences and ultimately behavior depend

solely on the incentives provided by the firm. The advisor’s best strategy in

the model takes the form of a rule based on a cutoff value for the signal, s∗.We show that participants will be advised to buy a fund product if and only

the advisor observes a signal s > s∗, and the value of s∗ that is implemented

depends on the choice of compensation. We refer to this threshold value of s∗

as the standard. An intuitive interpretation would be that s is a signal of risk

tolerance. Participants are recommended to purchase the risky mutual fund

product only if they meet the standards for risk-tolerance, i.e. only if the

advisor’s assessment of their risk-tolerance exceeds s∗ . Following the method

of Grossman and Hart(1983), the provider’s optimal compensation scheme

is obtained by computing agency costs for any level s∗ and then identifying

the least costly value of s∗.

4.1 Threshold-Setting

We first show that the firm can set the agent’s optimal response such that

having observed a signal s, the agent complies with a threshold standard,

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s∗, and recommends buying the mutual fund product only if s exceeds the

standard.

Proposition 4.1. The agent’s compensation scheme (w1, w2, w3) can be cho-

sen to implement a standard s∗ > 0 such that the agent recommends a sale

if s > s∗ and 0 otherwise.

Proof. For any signal s, the advisor’s expected compensation from a sale,

V (s), may be written as q(s)w2 + (1 − q(s))[(1 − φ)w2 + φw3]. This can be

rearranged to give

V (s) = w3 + [1 − φ(1 − q(s))](w2 − w3)]

If w2 > w3 then V (s) is strictly increasing and continuous in s. Furthermore,

if w2 > w1 > (1 − φ)w2, V (0) < w1 and V (1) > w1 . Then there exists a

cutoff signal s∗ > 0 such that V (s∗) = w1, where the advisor is indifferent

between making a sale or no sale.

4.2 Incentivizing Effort

In this model, suppose that advice effort is observable by the customer, but

not by the firm. By assumption, quh + (1 − q)ul < 0, so for any price p set

by the firm, customers will not purchase the product if the agent is seen to

shirk his advice effort. Consequently, any agent incentivized to provide sales

effort for a participantalso must find it optimal to exert advice effort.

Without exerting any effort, the agent can always earn w1. By exerting

sales effort cs, the agent interests a participantwith probability μ and then

has to exert further effort ca to observe s. For a given standard s∗, the agent

realizes the expected compensation V (s) if s > s∗. The agent thus exerts

effort only if the expected additional compensation μ∫ 1

s∗ [V (s) − w1]f(s)ds

exceeds the additional expected cost of effort, cs + μca.

The incentive constraint can then be written as∫ 1

s∗[V (s) − w1]f(s)ds ≥ cs

μ+ ca (4.1)

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4.3 Optimal Compensation and Agency Cost

We first show that the optimal (minimum cost) compensation scheme for any

standard s∗ takes the form of a base salary and a sales commission, both of

which are forfeited in the event of a complaint.

Proposition 4.2. To implement any standard s∗ > 0, the optimal (minimum

cost) compensation scheme comprises a base salary w and an additional sales

commission b such that

w =( cs

μ+ ca)[1 − φ(1 − q(s∗))]∫ 1

s∗ [q(s) − q(s∗)]f(s)ds(4.2)

and

b =( cs

μ+ ca)∫ 1

s∗ [q(s) − q(s∗)]f(s)ds(4.3)

In the event of an ex-postcomplaint, the provider pays the advisor nothing,

equivalent to levying a forfeit of w + b.

Proof. At the optimum, the incentive constraint equation 4.1 has to bind.

We can then substitute the expression for V (s) and the observation that

w1 = V (s∗) into 4.1, such that

∫ 1

s∗[V (s) − V (s∗)]f(s)ds =

cs

μ+ ca

which gives us in turn

w2 = w3 +

cs

μ+ ca∫ 1

s∗ [q(s) − q(s∗)]f(s)ds(4.4)

and

w1 = w3 +( cs

μ+ ca)[1 − φ(1 − q(s∗))]∫ 1

s∗ [q(s) − q(s∗)]f(s)ds(4.5)

Given the limited liability constraint w1, w2, w3 ≥ 0, the minimum com-

pensation scheme then sets w3 = 0. We can then express the compensation

scheme as w1 = w, w2 = w+b where b = w2−w1. This allows us to interpret

w ≥ 0 as a base salary, b ≥ 0 as a sales bonus. Substituting these parameters

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into 4.4 and 4.5 leads to the optimal compensation scheme in Proposition

4.2.

Finally, we check the two conditions given in Proposition 4.1 for the

existence of s∗ > 0 and verify that they hold. We want to check that w2 > w3

and w2 > w1 > (1 − φ). We can easily verify w2 > w3 since w + b > 0, and

w2 > w1, since w + b > w. Then, w1 > (1 − φ)w2 w > (1 − φ)(w + b) can be

written as bw

< φ1−φ

. Substituting w and b into our expression for the cutoff

signal V (s∗) = w1 gives

b

w=

φ(1 − q(s∗))1 − φ(1 − q(s∗)

<φ

1 − φ(4.6)

In this case, the base salary w, which is paid whether or not a sale is real-

ized, may be regarded as an information rent for implementing a particular

standard.

Proposition 4.3. The salary needed to ensure compliance with a particular

standard (i) increases in the standard s∗, (ii) increases in the cost of sales cs

(iii) increases in the cost of advice ca and also (iv) decreases in the frequency

of complaints or audits φ

Proof. By differentiation of Equation 4.2, applying Leibniz’ integral rule, we

finddw

ds∗= (

cs

μ+ ca)

dq(s∗)ds∗

∫ 1

s∗ [1 − φ(1 − q(s∗))]f(s)ds

φ[∫ 1

s∗ [q(s) − q(s∗)]f(s)ds]2> 0

The other first derivatives of Equation 4.2 are more straightforward

dw

dcs

=1 − φ(1 − q(s∗))

μ∫ 1

s∗ [q(s) − q(s∗)]f(s)ds> 0

dw

dca

=1 − φ(1 − q(s∗))∫ 1

s∗ [q(s) − q(s∗)]f(s)ds> 0

dw

dφ=

−( cs

μ+ ca)(1 − q(s∗)∫ 1

s∗ [q(s) − q(s∗)]f(s)ds< 0

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5 Basic Equilibrium

In what follows, we assume that plan participants are not able to observe the

fee structure (and by extension, the provider standard, s∗). The provider’s

best response function s∗(p) describes the firm’s willingness to sell at a given

standard as a function of price. In turn, the participant’s best response

function p(s∗) describes his willingness to pay as a function of his expected

standard. In equilibrium, the price p and the standard s∗ are jointly deter-

mined such that the firm sets s∗ optimally given the market price p, which

in turn reflects the correct expectation of s∗ by the participants.

5.1 Provider willingness to sell

The providers’ expected gross profits for any s∗ given price p can be written

ΠG = μ

∫ 1

s∗π(s)f(s)ds

where the expected profit from realizing a sale is the revenue less resource

costs and expected penalty, π(s) = p − k − ρ(1 − q(s)).

At the optimum, the incentive constraint equation 4.1 has to bind, such

that the advisor’s expected compensation for exerting effort net of his base

salary, is equal to cs + μca. The firms’ expected wage bill is therefore w +

cs + μca, and expected net profits are W = ΠG − w − cs − μca

The provider’s problem is then to choose s∗ to maximize expected net

profits W for a given value of p. Ignoring the corner solution s∗ = 0, the

first order condition with respect to s∗ gives a unique interior solution s∗

implicitly defined by

−f(s∗)μπ(s∗) =dw

ds∗(5.1)

Inderst and Ottaviani (2009) note that dwds∗ > 0 implies that π(s∗) < 0; i.e.

at the optimal standard s∗ the firm realizes a net loss on the marginal sale.

However, the total expected net profit is maximized because implementing

this standard reduces the wage cost needed to ex-ante properly incentivize

the agent.

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The firm’s standard decreases with the equilibrium price of the mutual

fund, but increases with the expected penalty from misselling and the prob-

ability of an inappropriate sale being discovered.

Lemma 5.1. The providers’ best response function s∗(p) is decreasing in p,

increasing in ρ and increasing in φ.

Proof. We define a function ψ = −f(s∗)μπ(s∗)− dwds∗ = 0 from Equation 5.1.

Since ∂ψ/∂s∗ < 0, then ∂ψ/∂p < 0, ∂ψ/∂ρ > 0 and ∂ψ/∂φ > 0, the results

above follow directly from the implicit function theorem2.

5.2 Participant willingness to pay

For any standard s, a sophisticated participant’s expected utility is q(s)uh +

(1−q(s))ul. For an expected standard s∗, the participant receives a purchase

recommendation with probability 1 − F (s∗). His willingness to pay for the

fund is equal to expected utility conditional on receiving the recommenda-

tion,

p(s∗) =

∫ 1

s∗[q(s)uh + (1 − q(s))ul]

f(s)

1 − F (s∗)ds (5.2)

Lemma 5.2. A sophisticated participant’s willingness to pay, p(s∗), is in-

creasing in the expected standard s∗, and increasing in both uh and ul.

Proof. We compute the partial derivative

∂p(s∗)∂s∗

=f(s∗)

1 − F (s∗)[p(s∗) − [q(s∗)uh + (1 − q(s∗))ul)] > 0 (5.3)

since for any expected standard s∗, the conditional expected utility p(s∗)over the range of signals greater than s∗ is greater than the expected utility

condition on the signal being exactly s∗, q(s∗)uh + (1 − q(s∗))ul. We also

note that ∂2p(s∗)∂uh

=∫ 1

s∗ q(s) f(s)1−F (s∗)

ds > 0 and∂2p(s∗)∂ul

=∫ 1

s∗(1−q(s)) f(s)1−F (s∗)

ds >

0.

2For explicit computation, see Appendix, Inderst and Ottaviani (2009)

15

Figure 5.1: Stylized Equilibrium

Proposition 5.3. In an equilibrium with no disclosure about (w, b), (p, s∗)is uniquely characterised by

p(s∗) =

∫ 1

s∗[q(s)uh + (1 − q(s))ul]

f(s)

1 − F (s∗)ds (5.4)

and

−f(s∗)μ[p − k − ρ(1 − q(s∗))] =dw

ds∗(5.5)

In equilibrium, the following must hold: firstly, the profit-maximizing

firm sets the maximum feasible price under the expected standard s∗, equal to

the participants’ maximum willingness to pay, such that p(s∗) = p. Secondly,

participant’s expected standard s∗ must be the realized signal that is optimal

for the firm s∗ = s∗(p). A stylized illustration of equilibrium is presented in

Figure 5.2.

16

6 Equilibrium with low participant financial

literacy

A straightforward interpretation of financial illiteracy (and a key concern

for misselling) is naivete. A naive participant interprets advice literally and

believes his expected utility to be uh conditional on receiving a buy recom-

mendation. Consequently, conditional on being told to buy, regardless of the

expected standard s∗, he is always willing to pay uh (see Figure 6).

Proposition 6.1. In an equilibrium with only naive participants, the price p

is the highest that the firm can charge, but the prevailing standard s∗ is lower

than in an equilibrium with only sophisticated (financially-literate) partici-

pants.

Proof. For an expected standard s∗, the financially illiterate participant re-

ceives a purchase recommendation with probability 1−F (s∗). The provider’s

best response function remains the same, but the customers’ demand curve

is now flat. In equilibrium, the provider will charge p = uh >∫ 1

s∗ [q(s)uh +

(1 − q(s))ul]f(s)

1−F (s∗)ds. Since dp > 0, by Lemma 5.1, there is also a resulting

fall in the equilibrium threshold standard s∗.

Figure 6.1: Stylized Equilibrium with Naive Participants

17

In this case, less financially literate consumers are twice disadvantaged:

they are more willing to pay for the product, leading to a higher equilibrium

product price, and also a correspondingly lower standard for advice. It is

important to note that this is not a general remark: the type of behavioral

bias is important, as different manifestations of financial illiteracy may not

lead uniformly to lower standards.

For instance, another interpretation of financial illiteracy is the failure

to appreciate the value of risky assets. Unlike the naive participant, in this

case, the financially illiterate participant may believe the utility of the high

type to be higher or lower than uh. In this case, the participants willingness

to pay, p(s∗) is higher or lower for any threshold s∗, than in the basic equi-

librium, By the same reasoning as above, the equilibrium price that prevails

is therefore higher or lower than the price in the basic equilibrium. Gen-

eral overconfidence on the part of participants therefore results in a higher

price and a lower threshold standard. Conversely, underconfidence leads to

lower demand, and results in a lower overall price and also a higher threshold

standard.

7 Policy Implications

7.1 External audits and penalties

In this model, regular audit requirements may be straightforwardly inter-

preted as a higher value for φ, i.e. a uniformly higher probability of dis-

covery when misselling occurs. A more stringent expected penalty may be

interpreted as a higher ρ. In equilibrium, the threshold standard s∗ is in-

creasing in the penalty ρ, and increasing in the quality of monitoring φ.

Changes in φ and ρ affect only the firm’s best response function, but leave

the consumer response unchanged. From Lemma 5.1, ds∗dρ

and ds∗dφ

are both

positive, resulting in the upward shift in s∗(p), as depicted in Figure 5.2. The

model therefore suggests that audits and penalties will have a direct effect

on raising standards, regardless of the financial literacy of the participant

population.

Changes in price due to higher standards, however, depends on the par-

18

ticipant population. For a sophisticated population, the higher prevailing

equilibrium standard s∗ is accompanied by a higher equilibrium price p, as

consumers are more willing to pay for the added security of the higher thresh-

old standard. There is no change in the equilibrium price if participants are

naive, since the firm is already charging as much as possible.

We note that in the absence of formal regulation, other mechanisms that

affect these parameters in the same way will have the same effect. For in-

stance, greater participant activism or a more well-functioning system of

complaints can raise φ, and therefore standards. Alternatively, if firms incur

a large reputation cost from misselling, this can raise the expected penalty

ρ.

7.2 Level compensation and task separation

We may interpret level-fee restrictions as a requirement for setting b = 0.

Assuming that the firm is not able to separately employ advisors and sales-

people, but relies only on a single agent who undertakes both tasks, this

constraint will significantly impact its activity. Without the sales commis-

sion, the agent will exert no effort either to contact participants or to observe

the signal s, and so the optimal value of w in this case is then also 0. The

firm has no incentives to offer the agent, and no customers are solicited.

Suppose that, as recent policy proposals, suggest, firms are able to com-

pletely separate the roles of advisor and salesperson, but still cannot monitor

the advisor’s effort.

Proposition 7.1. Compared to the baseline case, when advisors are sepa-

rated from sales, the firm’s best response results in a higher advice standard

s∗

Proof. In the separation case, the firm effectively reduces cs = 0. The advisor

still has to choose to expend ca in order to observe the signal but for any

standard s∗, the optimal w is lower. As before, recall we define a function

ψ = −f(s∗)μπ(s∗) − dwds∗ = 0 from Equation 5.1. We know from previously

that ∂ψ/∂s∗ < 0 , and differentiation of dwds∗ gives d2w

ds∗dcs> 0. This implies

∂ψ/∂cs < 0and from the implicit function theorem we then have ∂s∗∂cs > 0:

for any price p, the firm’s best response s∗ is higher.

19

Note that this result is general to a reduced cost of sales effort. In other

words, making it less effortful for advisors to meet clients will also result in

higher standards, for instance if the plan automatically matches participants

to advisors. However, even if advisors and salespeople are separated, a sales

commission may is be optimal.

Proposition 7.2. Even under task separation, if the effort of providing ad-

vice is privately costly and cannot be observed, non-zero commissions are still

optimal for any positive standard s∗

Proof. The firm’s optimal compensation scheme for implementing s∗ is b =caR 1

s∗ [q(s)−q(s∗)]f(s)ds> 0 as long as ca > 0

In the absence of a commission, the advisor will not be motivated to

expend costly unseen effort and therefore the participant will not purchase.

The only way to implement level-compensation in an incentive compatible

way is for the firm to (a) observe advisors’ efforts directly and pay compen-

sation conditional on observed effort or (b) reduce ca to zero. Option (a) is

equivalent to stating that the firm needs to resolve the fundamental infor-

mation asymmetry. Reducing advisors’ cost of effort is more difficult, but

some might argue that having advisors provide only generic assessment from

computer models can help achieve this goal. Realistically speaking, however,

it is not clear that such options are generally feasible, suggests that some

firms (particularly those that cannot separate advisors from salespeople) will

not find it optimal to do business.

7.3 Fee Disclosure Regulation

In the preceding analysis, s∗ and p are jointly determined in equilibrium,

given that compensation and s∗ itself are not observable. Suppose however,

that regulation mandates credible disclosure of (w, b). In this case, (w, b)

uniquely reveals s∗ to the participants. The best response function for par-

ticipants is then a function of the true s∗ rather than their expectations.

The firm now maximizes a profit function in which the price p is deter-

mined by participants’ best response to the firm’s own choice of standard,

20

rather than taken as exogenous, i.e. the firm sets s∗ to maximize

μ

∫ 1

s∗p(s) − k − ρ(1 − q(s))f(s)ds − w − cs (7.1)

This results in the following FOC for s∗,

μdp(s∗)ds∗

[1 − F (s∗)] − f(s∗)μπ(s∗) =dw

ds∗(7.2)

Equilibrium is thus defined by the participants’ best response function

5.2 and the new FOC, 7.2.Compared to the FOC under no-transparency

−f(s∗)μπ(s∗) = dwds∗ , the additional first term captures the impact of having

observable s∗. Intuitively, with the additional disclosure, firms can credibly

commit to a higher standard of advice, but will also as a result charge more.

Proposition 7.3. With sophisticated participants, disclosure increases stan-

dards, but also firm profits and prices

Proof. In this case, the additional first term μdp(s∗)ds∗ [1−F (s∗)] is always pos-

itive. All other parameters being held equal (including therefore dwds∗ ) , this

implies that under the new FOC, the equilibrium value of π(s∗) is higher

under transparency , for any value of s∗. This therefore also implies a higher

equilibrium price p for any s∗. Finally, given that participants’ best response

p(s∗) is unchanged, this also implies a higher prevailing equilibrium standard

s∗.

Proposition 7.4. With naive participants, disclosure will not affect the equi-

librium outcomes.

Proof. If participants are not financially literate, the FOC under no-transparency

(the basic equilibrium) and transparency are identical, since dp(s∗)ds∗ = 0. The

intuitive reasoning is that if naive participants take recommendations at face

value, disclosing the actual standard has no bearing on their behavior. Thus,

disclosure requirements are not likely to be effective if participants are too

naive to incorporate this information into their decisions.

The model then suggests that firms may have an incentive to support

disclosure regulation if participants are sophisticated enough to appreciate

21

the gain in credibility as a result. In this case, standards are also likely to

increase. However, if participants are not, there is no incentive for the firm

to support increasing disclosures, particularly if disclosure is costly; and in

this case there may be no appreciable gain in standards either.

8 Concluding Remarks

In this paper, we adapt the direct selling model of Inderst and Ottaviani

(2009) to the context of 401(k) plans, and examine its implications for some

of the leading policy proposals currently under discussion. The results of the

model underscore the basic tradeoff that firms face between cutting down on

misselling and sufficiently motivating advisors to provide valuable services.

Our extension to include financial literacy shows that differences in investor

sophistication can have significant implications for what prices and standards

ultimately prevail in the financial marketplace. The model suggests that pol-

icy tools such as monitoring, auditing and disclosure can have large effects

on standards, working indirectly through compensation, but directly manip-

ulating compensation may lead to compromises in agent incentives that affect

firms’ ability to do business. Other policy tools that could be discussed in

later work include the possibility of self-regulation.

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